1. Field of the Invention
The present invention relates to a multi-objective optimal design support technique used in the design of a slider shape of a hard disk and the like.
2. Description of the Related Arts
Along with the high-density/high capacity of a hard disk, a distance between a magnetic disks and a header has been more and more reduced. A slider design with a small amount of fly variations due to an altitude difference and a disk diameter position is required.
As represented as 2001 in FIG. 1A, a slider is installed in the tip lower part of an actuator 2002 moving on a magnetic disk in a hard disk and the position of a header is computed on the basis of the shape of the slider 2001.
When determining the optimal shape of the slider 2001, an efficient computation for simultaneously minimizing the function of flying height (2003 in FIG. 1A), roll (2004) and pitch (2005), so-called multi-objective optimization is required.
Conventionally, instead of directly handling a multi-objective optimization problem, a single-objective optimization in which as shown below, the linear sum f of terms obtained by multiplying each objective function f_i by weight m_i and its minimum value is computed, is performed,f=m—1*f—1+ . . . +m—t*f—t   (1)
Then, a function value f is computed while parameters p, q, r and the like, for determining a slider shape S shown in FIG. 1B are being modified little by little by a program, and the slider shape S in which the function value f is minimized is computed.
In the above equation, f depends on weight vector {m_i} In actual design, the minimum value of f for each modification value is computed while further modifying {m_i} and a slider shape is determined by comprehensively taking into consideration the balance between the minimum value and {m_i}.
In the multi-objective optimization process performed by the above-described method, the number of optimal solutions to be computed is not always one.
For example, when in the design of a certain product an objective function value 1 of “reducing its weight” and an objective function value 2 of “reducing its cost” are optimized, the objective function values 1 and 2 can take various coordinate values in two-dimensional coordinate system, as shown in FIG. 1C depending on how to give design parameters.
Since it is required that the objective function values 1 and 2 take small values independently (the product is light and inexpensive), a point on a line 2203 connecting computed points 2201-1, 2201-2, 2201-3, 2201-4 and 2201-5 shown in FIG. 1C or a point in its vicinity can be an optimal solution group. These are called Pareto optimal solutions. Of these computed values, the point 2201-1 corresponds to a model which is expensive but light, and the point 2201-5 corresponds to a model which is inexpensive but not light. However, since the points 2202-1 and 2202-2 can be made lighter and more inexpensive, they cannot be optimal solutions. These are called inferior solutions.
In this way, in a multi-objective optimization process, it is very important to be able to properly obtain a Pareto optimal solution. For that purpose, it is important for the Pareto optimal solution of a desired objective function to be able to properly visualize.
As a prior art for obtaining such a Pareto optimal solution, a so-called normal boundary intersection (NBI) method for computing a Pareto curved surface in multi-objective optimization (optimal curved surface) by a numerical analysis method and the like are known. In such a technique, for example, when in the above-described slider design, a certain design specification and factor parameters are given, the relation between desired objective function values (pitch, the amount of fly, etc.) can be plotted as shown in 2301 of FIG. 1D by numerically computing them.
As other prior arts, a technique for displaying a Pareto curve by points or plotting and a technique for displaying objective functions by a trade-off chart are also known, as shown in FIG. 1E.
Furthermore, the following Patent documents are also known. Patent document 1 discloses a technique for classify a plurality of design points in a design space by color and realizing three-dimensional plotting. Patent document 2 discloses a technique for realizing three-dimensional plotting by contour display. Patent document 3 discloses a technique for realizing two-dimensional plotting by a unified evaluation index vs. cost.
Patent document 1: Japanese Patent Application Laid-open No. 2005-70849
Patent document 2: Japanese Patent Application Laid-open No. 2003-39184
Patent document 3: Japanese Patent Application Laid-open No. 2004-118719
However, in the optimization technique of the single-objective function fin the earlier-described prior art, flying height computation which takes much time to conduct must be repeated. In particular, when probing up to the fine parts of a slider shape, the number of input parameters (corresponding to p, q, r and the like in FIG. 1B) becomes around 20 and 10,000 times or more of flying height computation are necessary. Therefore, optimization takes very much time.
Furthermore, in this method, the minimum value of f (and input parameter values for the minimum value) depends on how to determine weight vectors (m_1, . . . m_t). In actual design, a situation in which it is desired that f should be optimized for various sets of weight vectors frequently occurs. However, in the above-described prior art, since it is necessary to do an optimization computation accompanying expensive flying height computation over again from the beginning every time modifying a weight vector, the number of types of weight vectors to attempt is limited.
Furthermore, since the minimization of a function value f can be applied to only one point on the Pareto curved surface, it is difficult to predict an optimal relation between objective functions and also such information cannot be fed back to design.
As described above, conventionally, since a multi-objective optimization process itself takes very much time, it is difficult even to display a correct Pareto optimal solution.
In the earlier-described prior art of computing a Pareto curved surface by a numerical analysis method, if the feasible region is non-convex, it cannot be solved. If points (end points) being a source for computing a Pareto curved surface are close to each other, the algorism does not work well. Furthermore, in the acquisition of a Pareto optimal solution, since a simple plotting display is provided if objective function values are displayed as coordinates, as shown in FIG. 1D, it is difficult to determine where is located a Pareto optimal solution.
Furthermore, even in the prior art which is devised to display a Pareto optimal solution, as shown in FIG. 1E, the Pareto optimal solution is simply displayed. For example, when a Pareto optimal solution is obtained between two or three objective functions, a relation between an objective function and a design parameter cannot be obtained. Alternatively, the degree of contribution of another objective function cannot be obtained.